Does Gurobi support mathematical integers or is it limited to machine precision for Integer programs?

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Ryan Brummet

2019年07月22日 16:58

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Suppose that I have the very simple helloworld style integer program below:

 

Max X s.t.

X * W <= A
X <= 1
0 <= X


Where X is the integer variable (can be 0 or 1), and W and A are constant integers.

Suppose further, that W is very large, for example, 2251799813685248.

With such a large size, using standard primitives (like a 32 bit int) will cause problems.

Therefore, my question is does Gurobi support mathematical integers (i.e. no bounds and uses something like GMP under the hood) or is it limited to machine precision?

0

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  Greg Glockner

  • Gurobi Staff

  2019年07月22日 20:06 編集済み

  Gurobi uses standard mixed-integer programming (MIP) techniques: it solves MIP models via a series of continuous (linear programming) relaxations. All variables are therefore continuous (double) values; a value is considered an integer if it is within IntFeasTol of an integer value.

  Additionally, a large coefficient like 2251799813685248 will cause numerical problems for the underlying LP relaxation.

  (I moved this to the modeling topic).
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  Simranjit Kaur

  • Gurobi Staff

  2025年06月23日 03:24 編集済み

  This post is more than three years old. Some information may not be up to date. For current information, please check the Gurobi Documentation or Knowledge Base. If you need more help, please create a new post in the community forum. Or why not try our AI Gurobot?.

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